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Rational Closure Extension in SPO-Representable Inductive Inference Operators

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Logics in Artificial Intelligence (JELIA 2023)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 14281))

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Abstract

The class of inductive inference operators that extend rational closure, as introduced by Lehmann or via Pearl’s system Z, exhibits desirable inference characteristics. The property that formalizes this, known as (RC Extension), has recently been investigated for basic defeasible entailment relations. In this paper, we explore (RC Extension) for more general classes of inference relations. First, we semantically characterize (RC Extension) for preferential inference relations in general. Then we focus on operators that can be represented with strict partial orders (SPOs) on possible worlds and characterize SPO-representable inductive inference operators. Furthermore, we show that for SPO-representable inference operators, (RC Extension) is semantically characterized as a refinement of the Z-rank relation on possible worlds.

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Acknowledgements

This work was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation), grant BE 1700/10-1 awarded to Christoph Beierle as part of the priority program “Intentional Forgetting in Organizations” (SPP 1921). Jonas Haldimann was supported by this grant.

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Authors and Affiliations

  1. FernUniversität in Hagen, Hagen, Germany

    Jonas Haldimann & Christoph Beierle

  2. University of Cape Town and CAIR, Cape Town, South Africa

    Thomas Meyer

  3. University of Dortmund, Dortmund, Germany

    Gabriele Kern-Isberner

Authors
  1. Jonas Haldimann
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  2. Thomas Meyer
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  3. Gabriele Kern-Isberner
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  4. Christoph Beierle
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Correspondence to Jonas Haldimann .

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Editors and Affiliations

  1. TU Dresden, Dresden, Germany

    Sarah Gaggl

  2. Artificial Intelligence Research Institute - IIIA CSIC, Barcelona, Spain

    Maria Vanina Martinez

  3. Umeå University, Umeå, Sweden

    Magdalena Ortiz

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Haldimann, J., Meyer, T., Kern-Isberner, G., Beierle, C. (2023). Rational Closure Extension in SPO-Representable Inductive Inference Operators. In: Gaggl, S., Martinez, M.V., Ortiz, M. (eds) Logics in Artificial Intelligence. JELIA 2023. Lecture Notes in Computer Science(), vol 14281. Springer, Cham. https://doi.org/10.1007/978-3-031-43619-2_38

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  • DOI: https://doi.org/10.1007/978-3-031-43619-2_38

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  • Online ISBN: 978-3-031-43619-2

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